Question: Simplify the following expression: $\dfrac{33y^3}{22y}$ You can assume $y \neq 0$.
Explanation: $ \dfrac{33y^3}{22y} = \dfrac{33}{22} \cdot \dfrac{y^3}{y} $ To simplify $\frac{33}{22}$ , find the greatest common factor (GCD) of $33$ and $22$ $33 = 3 \cdot 11$ $22 = 2 \cdot 11$ $ \mbox{GCD}(33, 22) = 11 $ $ \dfrac{33}{22} \cdot \dfrac{y^3}{y} = \dfrac{11 \cdot 3}{11 \cdot 2} \cdot \dfrac{y^3}{y} $ $\phantom{ \dfrac{33}{22} \cdot \dfrac{3}{1}} = \dfrac{3}{2} \cdot \dfrac{y^3}{y} $ $ \dfrac{y^3}{y} = \dfrac{y \cdot y \cdot y}{y} = y^2 $ $ \dfrac{3}{2} \cdot y^2 = \dfrac{3y^2}{2} $